Journal of Operator Theory

Volume 51, Issue 1, Winter 2004 pp. 49-70.

The wavelet Galerkin operator

Authors: Dorin E. Dutkay
Author institution: Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242--1419, USA

Summary: We consider the eigenvalue problem $$R_{m_0,m_0}h=\lambda h,\quad h\in C(\mathbb{T}),\,|\lambda|=1,$$ where $R_{m_0,m_0}$ is the wavelet Galerkin operator associated to a wavelet filter $m_0$. The solution involves the construction of representations of the algebra $\mathfrak{A}_N$ --- the $C^*$-algebra generated by two unitaries $U,V$ satisfying $UVU^{-1}=V^N$ introduced in \cite{13}.

Keywords: Wavelets, Hilbert space, unitary operators, operator algebras, transfer operator, Ruelle operator, spectrum

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